Even though AX 2012 uses the Microsoft Solver Foundation which is not directly accessible to a developer, all data is stored within AX and can be worked with at will. See the follow overview of the data structure:
Note that most of the data is global, just the PCTemplateComponent table has company specific entries; the table is used for templates – as the name suggests – but also for the item references eg. for Configurator BOM lines.
The constraint based configuration is saved in relation to the configuration-number (InventDim.ConfigId), however all you see in the On-Hand form is the number.
If you want to see the full configuration that was entered by the user, you can add a simple button to the On-hand form (InventOnhandItem) and override the clicked() method with the following code: